Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 23, Problem 51CP
A solid insulating sphere of radius R has a nonuniform charge density that varies with r according to the expression ρ = Ar2, where A is a constant and r < R is measured from the center of the sphere. (a) Show that the magnitude of the electric field outside (r > R) the sphere is E = AR5/5ϵ0r2. (b) Show that the magnitude of the electric field inside (r < R) the sphere is E = Ar3/5ϵ0. Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
An infinitely long solid insulating cylinder of radius R has a uniform volume charge density of 0.99μC/m3.
If the magnitude of the electric field 0.302m from the axis of the cylinder is 3880N/C, what is R, the radius of the cylinder, in meters? Assume that R<0.302m, so the point of observation is exterior to the cylinder.
Consider two thin disks, of negligible thickness, of radius R oriented perpendicular to the x axis such that the x axis runs through the center of each disk. The disk centered at x=0 has positive charge density η, and the disk centered at x=a has negative charge density −η, where the charge density is charge per unit area.
What is the magnitude E of the electric field at the point on the x axis with x coordinate a/2?
Express your answer in terms of η, R, a, and the permittivity of free space ϵ0.
The volume charge density of a sphere of Radius R is directly related to the radius of the sphere as given by the equation p(r) = br where b is a positive integer. What would be expression for the electric field at r = 1/2 R from the center of the sphere?
Chapter 23 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 23.2 - Suppose a point charge is located at the center of...Ch. 23.3 - If the net flux through a gaussian surface is...Ch. 23 - A negatively charged rod of finite length carries...Ch. 23 - A positively charged disk has a uniform charge per...Ch. 23 - A uniformly charged ring of radius 10.0 cm has a...Ch. 23 - The electric field along the axis of a uniformly...Ch. 23 - Example 23.3 derives the exact expression for the...Ch. 23 - A uniformly charged rod of length L and total...Ch. 23 - A continuous line of charge lies along the x axis,...Ch. 23 - A thin rod of length and uniform charge per unit...
Ch. 23 - (a) Consider a uniformly charged, thin-walled,...Ch. 23 - A vertical electric field of magnitude 2.00 104...Ch. 23 - A flat surface of area 3.20 m2 is rotated in a...Ch. 23 - A nonuniform electric field is given by the...Ch. 23 - An uncharged, nonconducting, hollow sphere of...Ch. 23 - Find the net electric flux through the spherical...Ch. 23 - Four closed surfaces, S1 through S4 together with...Ch. 23 - A charge of 170 C is at the center of a cube of...Ch. 23 - (a) Find the net electric flux through the cube...Ch. 23 - A particle with charge of 12.0 C is placed at the...Ch. 23 - A particle with charge Q = 5.00 C is located at...Ch. 23 - Prob. 20PCh. 23 - Prob. 21PCh. 23 - Find the net electric flux through (a) the closed...Ch. 23 - Figure P23.23 represents the top view of a cubic...Ch. 23 - Determine the magnitude of the electric field at...Ch. 23 - Prob. 25PCh. 23 - Prob. 26PCh. 23 - A large, flat, horizontal sheet of charge has a...Ch. 23 - A nonconducting wall carries charge with a uniform...Ch. 23 - A uniformly charged, straight filament 7.00 m in...Ch. 23 - You are working on a laboratory device that...Ch. 23 - Consider a long, cylindrical charge distribution...Ch. 23 - Assume the magnitude of the electric field on each...Ch. 23 - A solid sphere of radius 40.0 cm has a total...Ch. 23 - A cylindrical shell of radius 7.00 cm and length...Ch. 23 - You are working for the summer at a research...Ch. 23 - You are working for the summer at a research...Ch. 23 - Find the electric flux through the plane surface...Ch. 23 - Prob. 38APCh. 23 - Prob. 39APCh. 23 - Show that the maximum magnitude Emax of the...Ch. 23 - A line of positive charge is formed into a...Ch. 23 - Prob. 42APCh. 23 - A sphere of radius R = 1.00 m surrounds a particle...Ch. 23 - A sphere of radius R surrounds a particle with...Ch. 23 - A slab of insulating material has a nonuniform...Ch. 23 - A sphere of radius 2a is made of a nonconducting...Ch. 23 - Prob. 47CPCh. 23 - Prob. 48CPCh. 23 - Review. A slab of insulating material (infinite in...Ch. 23 - Identical thin rods of length 2a carry equal...Ch. 23 - A solid insulating sphere of radius R has a...
Additional Science Textbook Solutions
Find more solutions based on key concepts
Whether two metal foil leaves an electroscope get opposite charge when the electroscope is charged.
The Physics of Everyday Phenomena
Is Earths inner core solid and the outer core liquid because the inner core is cooler than the outer core? Expl...
Conceptual Integrated Science
Choose the best answer to each of the following. Explain your reasoning. Which of these star clusters is oldest...
Cosmic Perspective Fundamentals
An aluminum calorimeter with a mass of 100 g contains 250 g of water. The calorimeter and water are in thermal ...
Physics for Scientists and Engineers, Technology Update (No access codes included)
2. Which of the following is the best example of the use of a referent? _
a. A red bicycle
b. Big as a dump tru...
Physical Science
Why is physics the most basic science?
Conceptual Physics: The High School Physics Program
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- An insulating solid sphere of radius a has a uniform volume charge density and carries a total positive charge Q. A spherical gaussian surface of radius r, which shares a common center with the insulating sphere, is inflated starting from r = 0. (a) Find an expression for the electric flux passing through the surface of the gaussian sphere as a function of r for r a. (b) Find an expression for the electric flux for r a. (c) Plot the flux versus r.arrow_forwardIf there is a a non-uniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−4r/3R)f or r≤R ρ(r)=0 for r≥R where ρ0 is a positive constant. What is the expression for the electric field in the region r <= R?arrow_forwardIf a solid insulating sphere of radius 50 cm carries a total charge of 150 µC uniformly distributedthroughout its volume, what is its a) volume charge density? What is the magnitude of the electricfield at b) 10 cm and c) 65 cm from the center of the sphere.arrow_forward
- A hollow conducting sphere with inner radius R and outer radius 2R has a non-uniform volume charge distribution in the region R<r<2R given by ρ(r)=(4C/m⁵)r². If R=0.564m, what is the magnitude of the electric field (in N/C) at r=3/2R?arrow_forwardA solid conducting sphere of radius R has a uniform charge distribution, with a density = Ps * r / R where Ps is a constant and r the distance from the center of the sphere. Prove a) the total charge on the sphere is Q = πPsR ^ 3 b) the electric field of the sphere is given by E = (1 / 4πε0) * (Q / R ^ 4) * (r ^ 2)arrow_forwardA solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r 1 = 6R the electric field has a magnitude E 0. What is the magnitude of the electric field at a radial distance r 2 = R/6 as a multiple of E 0 ?arrow_forward
- A solid sphere of insulating material with radius R=7.62cm�=7.62cm has a uniform volume charge density given by p(r) = { (p0 for r<=R), (0 for r > R)} where ρ0=296nC/m3. What is the magnitude, in newtons per coulomb, of the electric field at a distance r=3.28cm from the center of the sphere. What is the magnitude, in newtons per coulomb, of the electric field at a distance r=11.9cm from the center of the sphere.arrow_forwardA solid insulating sphere of radius R has a nonuniform charge density that varies with r according to the expression ρ = Ar2, where A is a constant and r < R is measured from the center of the sphere. (a) Show that the magnitude of the electric field outside (r > R) the sphere is E = AR5/5∈0r2. (b) Show that the magnitude of the electric field inside (r < R) the sphere is E = Ar3/5∈0. Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr.arrow_forwardA long, nonconducting, solid cylinder of radius 4.0 cm has a nonuniform volume charge density r that is a function of radial distance r from the cylinder axis: r =Ar2. For A = 2.5 mC/m5, what is the magnitude of the electric field at (a) r = 3.0 cm and (b) r = 5.0 cm?arrow_forward
- An insulating solid sphere of radius R = 6.0cm has a total positive charge Q uniformly distributed throughout its volume. The electric flux through a spherical Gaussian surface of radius r = 3.0cm is 2.26x105N.m2/C. How much charge (in units of μC) is enclosed by the Gaussian surface of radius r =3.0cm? What is the magnitude ( in units of 106N/C) of the E-field at the Gaussian surface of part (1)? What is the magnitude (in units of 106N/C) of the -field at surface of the sphere? (Example: If your answer is 3.4x106N/C, enter 3.4 in the answer box).arrow_forwardAn infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as ρ = ρ0(a - (r)/(b)) where ρ0, a, and b are positive constants and r is the distance from the axis of the cylinder. Use Gauss’s law to determine the magnitude of the electric field at radial distances (a) r < R and (b) r > R.arrow_forwardA disk of radius 2.5 cm has a surface charge density of 5.3 mC/m2 on its upper face.What is the magnitude of the electric field produced by the disk at a point on its central axis at distance z =12 cm from the disk?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Electric Fields: Crash Course Physics #26; Author: CrashCourse;https://www.youtube.com/watch?v=mdulzEfQXDE;License: Standard YouTube License, CC-BY